It's got nothing to do with your TV--the TV has no input as to what happens with your system, it just displays what it is told to.
When your Galactica game was last working, did you shut it off in the middle of playing a 2P game?
Where you playing 1-player when you quit the last time SMB was working?
Same question about SMW?
When you quit a VC game without hitting the Reset button on the Home menu, your Wii makes a quicksave of all the data from that game so far. Then, when you go to play the game again, it tosses you right back to that point. So, if you were in the middle of a Multiplayer Galactica game, you'll be in the middle of that game when you start the game up again.